WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICSphilsci.com/pdf/BOOK IV - Heisenberg.pdf · WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICS This book examines Werner

© Copyright 1995, 2005, 2016 by Thomas J. Hickey

WERNER HEISENBERG

AND THE SEMANTICS OF

QUANTUM MECHANICS

This book examines Werner Heisenberg’s interpretation of

quantum theory and the influence of Albert Einstein. Heisenberg’s semantical

view is the chrysalis of the contemporary pragmatist philosophy of language.

Heisenberg (1901-1976) was born in Wurzburg, Germany, and studied

physics at the University of Munich, where he wrote his doctoral dissertation

under Arnold Sommerfeld in 1923 on a topic in hydrodynamics. He became

interested in Niels Bohr’s atomic theory and went to the University of

Göttingen to study under Max Born. In 1924 he went to Bohr’s Institute for

Theoretical Physics in Copenhagen, where he developed the quantum matrix

mechanics in 1925, and then developed the indeterminacy principle in 1927.

From 1927 to 1941 he was a professor of physics at the University of

Leipzig. In 1932 he was awarded the Nobel Memorial Prize for Physics. In

the Second World War, he was the director of the Kaiser Wilhelm Institute

for Physics in Berlin. After the war he established and became director of the

Max Planck Institute of Physics initially at Göttingen, and then after 1958 at

Munich. His principal publications in which he set forth his philosophy of

physics consist of the “Chicago Lectures of 1930” published as The Physical

Principles of the Quantum Theory (1950, [1930]), Philosophical Problems of

Nuclear Science (1952) currently published under the title of Philosophical

Problems of Quantum Theory (1971), The Physicist’s Conception of Nature

(1955), an interpretative history of physics, Physics and Philosophy: The

Revolution in Modern Science (1958), his intellectual autobiography

published as Physics and Beyond (1971), and Across the Frontiers (1974).

Heisenberg’s philosophy of science was not significantly influenced by

the doctrines of academic philosophers, although he was a positivist early in

HEISENBERG

© Copyright 1995, 2005, 2016 by Thomas J. Hickey 2

his career and later rendered Bohr’s view of observation in neo-Kantian

terms, even though neither he nor Bohr were metaphysical idealists. The

formative intellectual influences on his philosophy were Einstein and Bohr.

These two philosophical influences were contrary to each other, and each

pulled Heisenberg’s thinking in opposite directions. Therefore, consider

firstly the philosophical views of Einstein and Bohr.

Heisenberg’s Discovery and Einstein’s Semantical Views

Reference was made in BOOK II in the discussion of Mach’s

philosophy about the influence of Einstein’s aphorism on Heisenberg’s

development of the indeterminacy relations. This episode in the history of

science, which Heisenberg relates in “Quantum Mechanics and a Talk with

Einstein (1925-1926)” in Physics and Beyond, is a watershed event for the

contemporary pragmatist philosophy of science. His description of his

personal experience and thought processes deserves close examination.

He had initially believed that he could develop a quantum theory

exclusively on the basis of observed magnitudes. He writes that in the

summer of 1924 he had attempted to guess the formula that might

successfully describe the line intensities of the hydrogen spectrum using

methods involving the idea of electron orbits, which he thought would be

successful in view of the previous work of Kramers in Copenhagen. When

use of these methods hit a dead end, he became convinced that he should

ignore the idea of electron orbits. He decided instead that he should treat the

frequencies and amplitudes associated with the spectral line intensities as

substitutes, because the line intensities are observable directly, while the

electron orbits are not. He was led to this approach because he recalled a

conversation years earlier in which a friend told him that Einstein had

emphasized the importance of observability in relativity theory. In May of

1925 Heisenberg suffered a severe hay fever attack and had to absent himself

from his academic duties. While recuperating on the island of Heligoland he

continued to work on the problem by considering nothing but observable

magnitudes, and during this period of isolation he developed his matrix-

mechanics version of quantum theory.

About a year later he was invited to give a lecture at the University of

Berlin physics colloquium to present his matrix mechanics. Einstein was in

the assembly, and after the lecture Einstein asked Heisenberg to discuss his

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views with him in his home that evening. In that discussion Einstein argued

that it is in principle impossible to base any theory on observable magnitudes

alone, because in fact the very opposite occurs: it is the theory that decides

what the physicist can observe. Einstein argued that when the physicist

claims to have observed something new, he is actually saying that while he is

about to formulate a new theory that does not agree with the old one, he

nevertheless must assume that the new theory covers the path from the

phenomenon to his consciousness and functions in a sufficiently adequate

way, that he can rely upon it and can speak of observations. The claim to

have introduced nothing but observable magnitudes is actually to have made

an assumption about a property of the theory that the physicist is trying to

formulate. Einstein objected that Heisenberg was using his idea of

observation as if the old descriptive language could be left as it is.

Heisenberg replied that Einstein was using language a little too strictly,

and that until there is a link between the mathematical quantum theory and the

traditional language, physicists must speak of the path of an electron by

asserting a contradiction, notably Bohr’s wave-particle “complementarity”

description. Heisenberg also replied by referencing Mach’s view that a good

theory is no more than a condensation of observations in accordance with the

principle of thought economy. Einstein replied that Mach thought a theory

combines complex sense impressions just as the word “ball” does for a child.

He also stated that the combination is not merely a psychological

simplification but is also an assertion that the ball really exists, because it

makes assertions about possible sense impressions that may occur in the

future. Einstein thus affirmed a realistic philosophy, and criticized Mach for

neglecting the fact that the real world exists, that our sense impressions are

based on something objective, and that observation cannot be just a

subjective experience. Heisenberg accepted Einstein’s realism on these

grounds, and admitted that theory reveals genuine features of nature and not

just of our knowledge.

In the “Preface” to his Physics and Beyond Heisenberg stated that his

purpose is to convey even to readers who are remote from atomic physics,

some idea of the mental processes that have gone into the genesis and

development of science. In the chapter titled “Fresh Fields (1926-1927)”

Heisenberg offers a description of his own mental processes in his

development of the indeterminacy relations. To the contemporary reader this

description has value apart from his systematic and explicit philosophy. Just

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as Newton attempted to philosophize about his work with his denial that he

created hypotheses, so too did Heisenberg attempt to philosophize about his

work with his own systematic and explicit philosophy of language – his

doctrines of closed-off theories and of perception. But the recollections of his

cognitive experiences in “Fresh Fields (1926-1927)” in Physics and Beyond

are not an attempt at a systematic philosophy. They are more simply his

recollection of his own cognitive experiences as a central participant in the

development of the quantum theory, and they are valuable as an historical

document. As it happens, in the contemporary pragmatist philosophical

perspective these recollections are far more valuable than Heisenberg’s

explicit attempt to philosophize on the nature of language and perception.

These writings reveal that his development of the indeterminacy

relations was occasioned by several historical circumstances. One of these

that he discusses in “Fresh Fields” was the development of the wave

mechanics by Schrödinger and its disturbing effects on the thinking of the

physicists at Copenhagen. The wave equation did not contain Planck’s

constant as did Heisenberg’s matrix mechanics, while Planck’s constant was

thought by Bohr and the Copenhagen physicists to be central and necessary

for any modern microphysical theory. Then Max Born, formerly a teacher of

Heisenberg, proposed a probability interpretation of the wave equation, such

that for each point in space and instant in time the wave equation gives the

probability of finding an electron at the given point and instant. The upshot

was that while neither the matrix mechanics nor the wave mechanics could be

rejected for empirical reasons, they nevertheless seemed to be logically

incompatible.

In addressing this problem Bohr and Heisenberg took different

approaches. Bohr attempted to admit simultaneously to the validity of both

theories by maintaining that both the classical wave and the classical particle

concepts used to describe the experimental observations are necessary for

characterizing atomic processes, even though in the language both of ordinary

discourse and of classical physics these two concepts are mutually exclusive.

A wave is spread out in space, while a particle is concentrated nearly at a

point. This semantic inconsistency became Bohr’s “complementarity”

principle. But Heisenberg relates that he did not like this approach, and that

he wanted a “unique”, that is, a consistent and unequivocal physical

interpretation of the magnitudes in the mathematical formalism, one that is

logically derivable from the matrix mechanics. Heisenberg reports that this

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objective was one of the reasons that led him to derive the indeterminacy

relations.

A second reason leading him to the indeterminacy relations was the

fact that neither the wave mechanics nor the matrix mechanics seemed

capable of explaining the observed track of the electron in the Wilson cloud

chamber. The cloud chamber developed by C.T.R. Wilson in 1912 consists of

a chamber containing a saturated vapor under pressure. When the pressure is

rapidly reduced, the vapor cools and becomes supersaturated, as the

temperature drops below the dew point. The passage of a charged particle,

i.e., an electron, through the vapor causes ion pairs to form droplets. A string

of these droplets mark the track of the passage of the charged particle. But

such ideas as tracks and orbits do not figure in the mathematical formulations

of the matrix mechanics, and the wave mechanics could only be reconciled

with the existence of a densely packed beam of matter, if the beam is spread

over volumes that are much larger than the dimensions of an electron. This

problem of the observed track in the cloud chamber led Heisenberg to reform-

ulate the questions he was asking himself in his statement of the problem. He

attempted to relate the observed track of the electron in the cloud chamber to

the mathematics of the matrix mechanics.

In February and March of 1927 Bohr was vacationing in Norway and

Heisenberg was again alone with his thoughts, as he had been when he had

earlier developed the matrix mechanics. At this time his attempt to relate the

cloud chamber observations to the matrix mechanics bought to mind his

discussion with Einstein the prior year in Berlin, and specifically Einstein’s

statement that the theory decides what the physicist can observe. In

“Fresh Fields” he describes his thinking processes when he attempted to

employ Einstein’s advice. Firstly he reconsidered the idea that what is

observed in the cloud chamber is a track. The idea of a track is a concept in

Newtonian physics. Therefore, when he thought that he was observing the

track of an election in the cloud chamber, the theory that was deciding what

was being observed was the Newtonian theory, not his quantum theory.

Then secondly after reconsidering the Newtonian observations and

recognizing that it is not necessary to think in Newtonian terms, he viewed

the phenomenon as merely a series of ill defined and discrete spots through

which the electron had passed, somewhat like the water droplets which of

course are very much larger than the dimensions of the electron. Then thirdly

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he reformulated his problem, and asked how quantum theory instead of

Newtonian theory can represent the fact that an electron finds itself

approximately in a given place and that it moves approximately with a given

velocity. Using Einstein’s thesis that the theory decides what the physicist

can observe, Heisenberg concluded that the processes involved in any

experiment or observation in microphysics must satisfy the laws of quantum

mechanics. The magnitude of the observed water droplets suggested room

for approximation for the minute electron, and Heisenberg asked whether it is

possible to imagine these approximations so close that they do not cause

experimental difficulties. He then derived the indeterminacy relations in

which the approximations are limited by Plank’s constant.

Heisenberg had formulated his indeterminacy principle by the time

Bohr had returned to Copenhagen from his vacation in Norway. Initially

Bohr objected to the idea, while at the same time Heisenberg disliked the

complementarity idea that Bohr had developed. After several weeks of

argument they finally agreed that the two approaches are related. The

indeterminacy principle reconciles at the microphysical level and in the

mathematical formalism of quantum mechanics, what cannot be avoided yet

what cannot be stated consistently in the language supplied by classical

physics and everyday language, which is suitable only to describe phenomena

at the macrophysical level. What is expressed consistently with the

mathematical formalism of the indeterminacy principle is the impossibility of

measuring simultaneously both the position and the impulse of the electron

with a degree of accuracy greater than the limit imposed by Planck’s

constant, a limit that is imposed by virtue of the nature of the microphysical

phenomenon itself and not merely by limits of measurement technique. What

are described inconsistently at the macrophysical level and in the language of

classical physics by means of complementarity, are the observable wave and

particle manifestations of the unitary phenomenon. This concession to Bohr

was at variance to Heisenberg’s acceptance of Einstein’s semantical thesis

that the theory decides what the physicist can observe. Heisenberg tried to

reconcile the dilemma, but never did.

Heisenberg’s description, which is based on his own experience of the

interpretative character of all perception and observation and of the rôle of

scientific theory in determining the interpretation, articulates one of the most

characteristic features of the contemporary pragmatist philosophy of science.

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It is more valuable than Duhem’s exemplification of the theoretical

interpretation of the laboratory apparatus in the opening passages of the

chapter titled “Experiment in Physics” in Aim and Structure of Physical

Theory, not only because Duhem’s explanation is positivist with his two-tier

semantics, but also because Heisenberg’s description of his experiences is

given in the context of his development of the indeterminacy principle, one of

the most noteworthy achievements of twentieth-century physics.

As it happens, Heisenberg did not like the pragmatism he encountered

at the University of Chicago during his visit to the United States and

described in “Atomic Physics and Pragmatism (1929)” in Physics and

Beyond. Even though his description of the interpretative character of

perception and observation actually contributed to the contemporary

pragmatism, Heisenberg himself was still influenced by Bohr in ways that

impeded his developing a philosophy of language that is consistent with

Einstein’s thesis that theory decides what the physicist can observe. This

influence places Heisenberg’s explicit philosophy of science closer to the

positivist philosophy than either Einstein’s or the pragmatists’ views. This

influence originated in Bohr’s naïve naturalistic philosophy of the semantics

of language. And the result was Bohr’s thesis of “forms of perception” and

Heisenberg’s consequent neo-Kantian rendering of Bohr’s philosophy of

perception.

Heisenberg’s Discovery and Einstein’s Ontological Criteria

An ontology consists of the entities and aspects of the real world that

are described by the semantics of a discourse, such as a scientific theory that

is believed to be true. Unlike Bohr, who took an instrumentalist view of the

equations of the quantum theory, Heisenberg maintained that quantum theory

describes ontology, that is, that the equations constituting the language of the

theory describe aspects of the real world. Thus he maintained that the

quantum theory describes nondeterministic microphysical reality and the

Copenhagen wave-particle duality, the thesis that wave and particle manifest

two aspects of the same physical entity and do not represent two separate

physical entities.

Initially, however, Heisenberg’s ontological views were not based in

the language of the mathematically expressed quantum theory, but were based

in the everyday language that can be used to express experimental findings.

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In the opening sentence of the “Introduction” chapter of his Physical

Principles of the Quantum Theory (1930), a book based on lectures he gave

at the University of Chicago in the Spring of 1929, Heisenberg says that the

experiments of physics and their results can be described in the language of

daily life. He adds that if the physicist did not demand a theory to explain his

results and could be content with a description of the lines appearing on

photographic plates, then everything would be simple and there would be no

need for an epistemological discussion. He states that difficulties arise only

in the attempt to classify and synthesize the results, to establish the relations

of cause and effect between them – in short, to construct a theory.

Heisenberg maintained that the everyday description of certain

experimental findings implies the Copenhagen ontology, and he proceeds to

give a brief description of several experiments including Young’s two-slit

experiment, which show that both matter and radiation sometimes exhibit the

properties of waves and at other times exhibit the properties of particles. He

notes that it might be postulated that two separate entities, one having all the

properties of a particle and the other having all the properties of wave motion,

are combined in some way. But he then adds that such a theory is unable to

bring about the “intimate relation” between the two entities, which seems

required by the experimental evidence. He argues that wave and particle are

a single entity, and that the apparent duality, the properties described in

Newtonian mechanics as “wave” and “particle”, is due to the limitations of

language. Such recourse to the limitations of language reveals the influence

of Bohr’s philosophy. For Heisenberg both quantum experiments and

quantum mechanics redefines the meaning of the word “entity”. Other

physicists such as Einstein, de Broglie, and Bohm did not agree with

Heisenberg’s view that there is any such compelling experimental evidence

for the Copenhagen duality ontology. Both philosophers and scientists have

had different ontological commitments, often because they maintain different

philosophies of language.

Einstein’s ontological view influenced Heisenberg’s ontological ideas.

Therefore briefly consider Einstein’s views. It may be said that Einstein had

two different ontological criteria for physics, one explicitly set forth by him,

and another that he tacitly used and which therefore may be called his implicit

criterion. In Newtonian physics and in relativity theory these two different

criteria are not easily distinguished, because in each case they yield similar

ontologies, but in quantum theory they yield fundamentally different

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ontologies. Einstein’s explicit ontological criterion for deciding what is

physically real is set forth in his “Can Quantum Mechanical Description of

Physical Reality be Considered Complete?” in Physical Review (1935), in his

“Physics and Reality” in The Journal of the Franklin Institute (1936), and in

his “Reply to Criticisms” in Albert Einstein (ed. Schilpp, 1949). There are

several statements.

One that he states as his “programmatic aim of all physics” is his

criterion of logical simplicity, which he sets forth as the aim of science: The

aim of science is a comprehension as complete as possible of the connections

among sense impressions in their totality, and the accomplishment of this aim

by the use of a minimum of primary concepts and relations. He goes on to

say that the essential thing about the aim of science is to represent the

multitude of concepts and theorems that are close to experience, as theorems

logically deduced from and belonging to a basis as narrow as possible, of

axioms and fundamental concepts that themselves can be chosen freely. This

is a coherence concept of the aim of science as the logical unity of the world

picture, and it might be described as an aspiration to what today is called a

“theory of everything”. Einstein interprets the history of physics as an

evolution under the direction of this aim of science. This criterion requires

that microphysical and macrophysical theories affirm one single consistent

ontology, and use the same basic concepts of what is physically real. Einstein

thus maintains that the conviction that deterministic field theory is unable to

give a solution to the molecular structure of matter and to the quantum

phenomenon, is a false prejudice. He demands that the ontology of field

theory supply this uniform fundamental ontology, and he uses this explicit

ontological criterion to criticize the nondeterministic Copenhagen

interpretation.

In a famous article titled “Can Quantum Mechanical Description of

Physical Reality be Considered Complete?” in Physical Review co-authored

with Podolsky and Rosen, Einstein describes the Copenhagen interpretation

as “incomplete”. By this he meant that further research is needed to make

quantum theory consistent with the ontology of field physics, the ontology of

deterministic causality and of the physical space-time continuum in four

dimensions. The argument in this paper, often called the “EPR argument”

after the three co-authors, includes a thought experiment, which is based on

explicit criteria for completeness and for physical reality. The completeness

criterion says that a physical theory is complete, only if every element of the

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physical reality has a counterpart in the physical theory. The criterion for

physical reality in turn is that if without in any way disturbing a system, one

can predict with certainty the value of a physical quantity, then there exists an

element of physical reality corresponding to this physical quantity. This

criterion’s reference to independence of any act of observation is repeated in

a later statement of the programmatic aim of all physics in “Remarks” in

Schilpp’s Albert Einstein: Philosopher-Scientist. The thought experiment in

the EPR argument attempts to demonstrate that the quantum theory’s

satisfaction of the reality criterion does not result in satisfaction of the

completeness criterion.

The stated criteria for completeness and for physical reality are defined

such that field theory satisfies both criteria while quantum theory does not.

The point of departure, the basic premises of the argument, is Einstein’s

ontological preferences. In an article with the same title also appearing in

Schilpp’s Albert Einstein Bohr argued that the phrase “without in any way

disturbing a system” in Einstein’s criterion for physical reality is ambiguous,

because its meaning in classical physics is not the same as that in quantum

physics. Bohr maintained that in quantum measurements the object measured

and the observing apparatus form a single indivisible system that defies any

further analysis at the quantum level. A large literature developed around the

technicalities of the physical thought experiment, but in practice even today

many physicists chose their ontological premises according to their

preferences about the ontological conclusions, depending on whether one

agreed or disagreed about Einstein’s view that quantum theory must have the

same ontology as field physics.

On the other hand Einstein’s implicit ontological criterion was

operative in his development of the special theory of relativity. This criterion

(stated explicitly) is that the empirically adequate scientific theory must be

interpreted realistically. Unlike Einstein’s explicit criterion, which

subordinates a scientific theory and its interpretation to a preconceived

ontology, the implicit criterion subordinates ontological commitment to the

outcome of empirical scientific criticism. This is the contemporary pragmatist

view, which Quine calls “ontological relativity”. Heisenberg applied this

same ontological criterion to the mathematical expressions of the quantum

theory to defend the Copenhagen dualistic ontology against Einstein’s

criticism based on the latter’s explicit ontological criterion for physical

reality. In this defense based on the mathematical language of the quantum

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theory instead of the everyday language of the microphysical experiments,

Heisenberg referenced Einstein’s realistic interpretation of the Lorentz

transformation equation. In his discussions about Einstein’s special theory of

relativity in Physics and Philosophy and in Across the Frontiers Heisenberg

describes as the “decisive” step in the development of special relativity,

Einstein’s rejection of Lorentz’s distinction between “apparent time” and

“actual time” in the interpretation of the Lorentz transformation equation, and

Einstein’s taking Lorentz’s “apparent time” to be physically real time, while

rejecting the Newtonian concept of absolute time as real time. In other words

this decisive step consisted of taking the Lorentz transformation equation

realistically, and of letting it describe the ontology of the physically real due

to its empirical adequacy.

Nowhere does Heisenberg write that he was consciously imitating

Einstein at the time Heisenberg developed the indeterminacy relations. But in

his “History of Quantum Theory” in Physics and Philosophy he describes his

use of the same strategy. In this description of his thought processes

Heisenberg does not refer to his conversation with Einstein in Berlin in 1926.

He states that his thinking in the discovery experience of the indeterminacy

principle consisted of his turning around a question. Instead of asking himself

how one can express in the Newtonian mathematical scheme a given

experimental situation, notably the Wilson cloud chamber experiment, he

asked whether only such experimental situations can arise in nature as can be

described in the formalism of the matrix mechanics. The new question is

about what can arise or exist in reality. Later in “Remarks on the Origin of

the Relations of Uncertainty” in The Uncertainty Principle and Foundations

of Quantum Mechanics (p. 42.) he explicitly states that this meant that there

was not a Newtonian path of the electron in the cloud chamber. Heisenberg’s

strategic answer to the new question, the indeterminacy relations, resulted

from this realistic interpretation of the quantum theory. Similar remarks are

to be found in “The Development of the Interpretation of the Quantum

Theory” in Pauli’s Niels Bohr and the Development of Physics (P. 15) where

Heisenberg says that he inverted the question of how to pass from an

experimentally given situation to its mathematical representation, by using the

hypothesis that only those states that can be represented as vectors in Hilbert

space can occur in nature and be realized experimentally. And he

immediately adds that this method had its prototype in Einstein’s special

theory of relativity, when Einstein had removed the difficulties of

electrodynamics by saying that the apparent time of the Lorentz

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transformation is real time. He similarly assumed in quantum mechanics that

real states can be represented as vectors in Hilbert space (or as mixtures of

such vectors), and that the indeterminacy principle is the simple expression

for this assumption.

If at the time he developed the indeterminacy principle, Heisenberg

was not consciously imitating the discovery strategy that Einstein used for

development of special relativity, it is nevertheless not difficult to imagine

how Heisenberg hit upon it independently. For the realist it is a small step

from Einstein’s semantical thesis that theory decides what can be observed, to

the ontological thesis that theory decides what is physically real, where the

theory in question is empirically warranted, as was Heisenberg’s matrix

mechanics. This strategy in which the empirical adequacy of a scientific

theory as revealed by scientific criticism decides the ontology to be accepted,

is a reversal of the more traditional relation in which currently accepted

ontological and metaphysical views are included among the criteria for

scientific criticism, and operate prior to or even in disregard of the outcome of

empirical criticism. Heisenberg explicitly compares his realistic interpretation

of quantum theory to Einstein’s realistic interpretation of the Lorentz

transformation equation, when he defends the ontology of his Copenhagen

interpretation against Einstein’s explicit ontological criterion for physical

reality.

In his “Criticism and Counter-proposals to the Copenhagen

Interpretation of Quantum Theory” in Physics and Philosophy Heisenberg

characterizes the ontology advanced explicitly by Einstein as the ontology of

“materialism”, which he says rests upon the “illusion” that the kind of

existence familiar to us, the direct actuality of the world around us, can be

extrapolated into the atomic order of magnitude. In the closing paragraphs of

this chapter of his book he states that all counterproposals offered in

opposition to the Copenhagen interpretation must sacrifice what he calls the

position-momentum symmetry properties of the quantum theory. He

explicitly states that like Lorentz invariance in the theory of relativity, the

Copenhagen interpretation cannot be avoided, if these symmetries are held to

be genuine features of nature.

Another example of Heisenberg’s practice of scientific realism is his

potentia ontology given in his summary of the Copenhagen interpretation of

the quantum theory in “The Copenhagen Interpretation of Quantum Theory”

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in his Physics and Philosophy. This might be taken as his redefinition of the

meaning of “entity”. Heisenberg invokes Aristotle’s idea of potentia to

express the thesis that wave and particle do not appear simultaneously, and

are wave or particle manifestations of the same entity. His interpretation of

the probability function is that it has both a subjective and an objective

aspect. The subjective aspect makes statements about the observer’s

incomplete knowledge, while the objective aspect makes statements about

what Heisenberg calls “tendencies” and “possibilities”, and it is in this latter

aspect that he refers to the idea of potentia. The probability function in the

quantum theory is subjective and represents incomplete knowledge, because

observers’ measurements are always inaccurate. The subjective reason that

they are inaccurate is the ordinary errors of measurement, the empirical

underdetermination that occurs both in both classical physics and quantum

physics. But the objective reason is distinctive to quantum physics, and it is

the inaccuracy caused by a disturbance introduced by the apparatus in the

measurement process.

Heisenberg illustrates this objective aspect by means of an ideal

experiment involving a gamma-ray microscope used to observe an electron.

In the act of observation at least one quantum of the gamma ray must have

passed the microscope, and must first have been deflected by the electron.

Therefore the electron must have been impacted by the quantum and must

have changed its momentum. The indeterminacy relations give the

indeterminacy of this momentum change. When the probability function is

written down, it includes both the objective and subjective inaccuracies, and

there must be at least two such disturbing observations in an atomic

experiment. The objective element in the probability function is not like the

description of motion in classical physics. The classical physicist would like

to say that between the initial and the second observation the electron has

described an unknown path. But Heisenberg says that between the two

observations the electron has not described any path in space and time, since

the electron has not been anywhere. The probability function does not

represent a course of events in the course of time, but rather represents

statistical possibilities or tendencies, which are actualized by the second act

of observation. The transition from the possible to the actual takes place with

the act of observation involving the interaction of the electron with the

measuring device. Heisenberg also notes that the transition applies to the

physical and not to the psychological act of observation, and that certainly

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quantum theory does not contain “genuine subjective features” in the sense

that it introduces the mind of the physicist as a part of the atomic event.

Heisenberg attributes the objective aspect of the quantum theory to

duality, which he construes as a transition from possible to actual. In his

Physics and Philosophy Heisenberg illustrates duality by the two-slit

experiment, the historic interference experiment firstly performed by Thomas

Young in 1801. It involves passing monochromatic light through a screen

with two holes or slits in it, and then registering the light on a photographic

plate. Viewed as a wave phenomenon there are primary waves entering the

slits, and then there are secondary spherical waves starting from the two slits,

which interfere with each other to produce an interference pattern on the

photographic plate. But the registration on the plate is a quantum process, a

chemical reaction. If the quantum particle passes through either slit, the other

one would normally be viewed as irrelevant. But the existence of the other

slit is in fact relevant, because the photographic plate registers the

interference pattern. Therefore the statement that any light quantum must

have gone through either just one or just he other slit is problematic.

Heisenberg maintains that this problematic outcome shows that the concept of

the probability function does not allow a description in space and time of

what happens between the two observations. The description of what

“happens” is restricted to the measurement observation process in which

there occurs the transition from the possible or potentia to the actual. David

Bohm had also proposed construing indeterminacy realistically as potentiality

in his Quantum Theory (1951), written while he accepted the Copenhagen

interpretation and before proposing his alternative hidden-variables thesis.

But Heisenberg does not reference Bohm for his own thesis of potentia, and

he seems to have derived the idea independently, probably from his reading

of Aristotle’s philosophy.

Bohr’s Influence on Heisenberg and Issues with Einstein

Niels Bohr was one of the leading atomic physicists of the first half of

the twentieth century. He had studied in England under J.J. Thompson and

Lord Rutherford, and received the Nobel Memorial Prize for Physics in 1922

for his theory of the structure of the atom. He founded the Copenhagen

Institute for Theoretical Physics in 1920, and as its director was actively

recruiting talented staff members, when he accepted an invitation to deliver a

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series of lectures on atomic physics at the University of Göttingen in the

summer of 1922.

In “Quantum Theory and its Interpretation” in Niels Bohr (1963)

Heisenberg reports that he first met Bohr at these Göttingen lectures, which

he attended with his teacher, Arnold Sommerfeld. At the time Heisenberg

was a twenty-two year old student at the University of Munich. Heisenberg

came to Bohr’s attention, because in the discussions following one of the

lectures, he dissented from Bohr’s optimistic assessment of a theory

developed by Kramers at Copenhagen. Heisenberg relates that Bohr was

sufficiently worried about the objection, that after the discussion he asked

Heisenberg to take a walk with him for a conversation. During the walk Bohr

talked about the fundamental physical and philosophical problems of modern

atomic theory.

The encounter resulted in an invitation for Heisenberg to visit the

Institute at Copenhagen for a few weeks, and later to hold a position.

Heisenberg describes Bohr as primarily a philosopher rather than a physicist,

and he states that he found Bohr’s philosophy to be fascinating, although he

also states that he and Bohr had different views on the rôle of mathematics in

physics.

Bohr’s philosophy of atomic physics is set forth in his Atomic Physics

and the Description of Nature (1934), “Discussions with Einstein” in Albert

Einstein (ed. Schilpp, 1949), Atomic Physics and Human Knowledge (1958),

and Essays 1958/1962 on Atomic Physics and Human Knowledge (1963).

Bohr’s philosophical views may have been influenced by some casual reading

of the philosophical literature, but he never references any philosopher in his

writings. His views seem largely to be the product of his own reflections on

his research in atomic physics and on the work of his staff at Copenhagen. In

“Quantum Theory and Its Interpretation” Heisenberg states that Bohr had

developed views on the semantics of language and scientific theory many

years before he met Bohr and before he developed his matrix mechanics.

Bohr’s mature philosophy of science included two theses: Firstly that

the mathematical formalisms of microphysics cannot describe the

microphysical domain that lies beyond ordinary experience. Secondly that

the only language that is capable of a descriptive semantics is the language of

ordinary discourse and its refinement in classical Newtonian physics.

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Heisenberg did not accept the first thesis, because he had a different concept

about the abstract nature of mathematics. But Bohr’s second thesis had a

lifelong influence on him, an influence that had a retarding effect on his

development of his own philosophy of microphysics.

Bohr gives various reasons why in his view the mathematical

formalisms of microphysics have no descriptive semantics and are only

symbolic instruments for making calculations and predictions. One reason

given in “Discussions with Einstein” is the occurrence of a complex number

in the formalism. Apparently he believed that reality could be described only

by equations having variables and parameters that admit only real numbers.

Another reason given in “The Solvay Meetings and the Development of

Quantum Theory” (1962) in his Essays 1958/1962 is the interpretation of the

statistical wave function in a configuration space of more than four

dimensions. Like Einstein, Bohr believed that real physical space-time has no

more than four dimensions.

But the basic reason why Bohr interpreted the mathematical formalism

of quantum theory instrumentally is his belief that only the language of

everyday discourse and its refinement in classical physics can have

descriptive semantics. He maintained that ordinary language and classical

physics must be used to describe any experimental set up in physics, while at

the same time he believed that classical physics is too limited to describe the

microphysical domain beyond ordinary experience. It is limited not only

because Newtonian physics is inadequate as a microphysical theory, but also

due to the inherent nature of human cognitive perception. This is a

philosophy of the semantics of language that is a naturalistic thesis. Due to

Bohr’s philosophy of perception, Einstein as well as many philosophers of

science were led to conclude that Bohr’s philosophy of science is positivist.

If Bohr’s philosophy of science is a positivist philosophy, it is a

peculiar one. His statements of his philosophy that are most often referenced

in this connection by philosophers of science are those in Atomic Physics and

the Description of Nature. In the opening “Introductory Survey (1929)” he

states that both relativity theory and quantum theory are concerned with

physical laws that lie beyond ordinary experience, and which therefore

present difficulties to our “accustomed forms of perception”. In quantum

theory the limitations of these forms of perception are revealed by the need

for complementary, the inconsistent Newtonian description of the quantum

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phenomenon as both a wave and a particle. Both of these two forms based

on classical physics are necessary for a complete description, even though

they are inconsistent in classical physics. Yet these “customary” forms of

perception cannot be dispensed with, since all human cognitive experience

must be expressed in terms of them. The fundamental concepts of classical

physics therefore will never become superfluous for the description of

physical experience; they must be used to describe experiments and to relate

the mathematical symbolisms to the perceptions in experience.

In Einstein’s attack on Bohr’s philosophy of quantum theory the central

issue is the ontology of the Copenhagen interpretation, which Einstein

critiqued with his programmatic aim of all physics. The explicit criterion set

forth in the programmatic aim of science is the “complete” description of any

individual situation, as it supposedly exists irrespective of any act of

observation or substantiation. Accordingly he characterized the Copenhagen

interpretation as a version of Bishop Berkeley’s idealist thesis “esse est

percipi”, a characterization that is not accurate, because Bohr did not

maintain that the atomic phenomenon is produced by a cognitive process but

rather by the physical processes of measurement in the experimental set up.

In this matter Einstein seems to have confused an epistemological issue with a

physical one.

But Bohr is not blameless for the confusion. For example in

“Introductory Survey (1929)” he opens with statements emphasizing the

subjectivity of all experience and the difficulties in distinguishing between

phenomena and their observation; and he concludes the chapter with the

statement that “to be” and “to know” lose their unambiguous meanings.

From an epistemological viewpoint some of Bohr’s statements are ambiguous

as to whether he is advancing a realist or an idealist philosophy. Some of

Heisenberg’s earlier statements are also suggestive of an idealist position.

For example he writes in the opening chapter of The Physicist’s Conception

of Nature, that since we can no longer speak of the behavior of the particle

independently of the process of observation, the natural laws formulated in

the quantum theory no longer deal with the elementary particles themselves,

but only with our knowledge of them. But later Heisenberg is very clear

about avoiding any metaphysical idealism. In “The Copenhagen

Interpretation of Quantum Theory” in Physics and Philosophy he states

explicitly that quantum theory does not contain genuinely subjective features,

since it does not introduce the mind of the physicist as part of the atomic

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event, and that the transition from possible to actual in the act of observation

is in the physical and not the psychical act of observation.

Any metaphysical idealist/realist ambiguity notwithstanding, however,

Einstein’s central ontological thesis is that the statistical quantum theory is

incomplete in the sense that further theoretical research is necessary, in order

to develop a complete theory that would give Heisenberg’s indeterminacy

relations a status in future physics, which he thought should be analogous to

the status had by statistical mechanics. It is noteworthy that Einstein admits

the indeterminacy principle is not empirically incorrect, even as he rejects the

Copenhagen nondeterministic ontology, because it does not conform to his

explicit ontological criterion. In the 1949 “Reply to Criticisms” Einstein

conceded that his incompleteness thesis is the minority view among

physicists; many contemporary philosophers as well as physicists have accep-

ted the indeterminacy thesis of the Copenhagen interpretation of the statistical

quantum theory, and have rejected the deterministic ontology advocated by

Einstein. When confronted with the dilemma of having to choose between an

established ontological criterion and a new but empirically adequate quantum

theory, both the contemporary physicists and the contemporary pragmatist

philosophers of science opt for the latter, contrary to Einstein’s arguments for

the former.

In addition to the ontological issue between Bohr and Einstein about

what is physically real, there is also a related epistemological issue about the

relation between sense perception and intellectual concepts. Einstein had

portrayed Bohr as a positivist due to Bohr’s views about perception and the

semantics of language. This portrayal is debatable, because positivists do not

usually speak of what Bohr called “forms of perception”, and particularly

about the limitations of such forms of perception for physics. But in his 1934

book Bohr writes of the necessity of these forms of perception for science to

reduce our “sense impressions” to order. Even though Einstein himself uses

the phrase “sense impressions” in his statement of the aim of science in

“Physics and Reality” in 1936, he seems to have taken Bohr’s discussion

referencing sense impressions to mean that there are no concepts or

categories in perception.

Einstein opposed this view, and stated in 1949 in his “Reply to

Criticisms” that thinking without positing categories and concepts is as

impossible as breathing in a vacuum. He furthermore states that his

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philosophy differs from Kant’s since he does not view categories as

unalterable and as predetermined by the faculty of understanding, but rather

views them as “free conventions”. The philosopher of science may ask

whether Einstein’s neo-Kantian views without Kant’s idealism and a priorism

is still recognizably Kantian. But the point to be emphasized is that Einstein’s

thesis that concepts are necessary for perception and that they are free

conventions amounts to a restatement of what he told Heisenberg in 1926,

when he said that theory decides what the physicist can observe. In this

earlier statement Einstein might consistently have told Heisenberg that

observation without theory is as impossible as breathing in a vacuum.

Perhaps it was in response to Einstein’s criticisms in these matters that Bohr

refrains in his later writings from using the phrase “sense impressions”.

Instead Bohr merely describes the concepts of classical physics as a

refinement of the concepts of ordinary discourse, so he is no longer

misunderstood as saying that perception occurs without any concepts.

Nonetheless there is still a fundamental difference between the

semantical views of Bohr and Einstein. Einstein’s thesis that concepts are

free conventions is intended to mean that there are none of the inherent

limitations in observation or in language that Bohr had maintained. In Bohr’s

phrase “customary forms of perception”, the term “customary” does not mean

the same thing as the term “convention” in Einstein’s phrase “free

conventions”. The limitations that Bohr said these customary forms of

perception impose on descriptive language are not temporary limitations,

which will be removed with the change in language customs resulting from

the further development of theory. Rather these limitations are inherent in the

nature of the human cognitive processes of perception and consequently in

the semantics of descriptive language. They are therefore permanent. There

is no such permanence according to Einstein’s view; the free conventions of

human thought, in the concepts and categories in language and scientific

theory, are not only conventions that are free to change, but are destined to

change with the advancement and further development of scientific theory.

The difference between Bohr’s and Einstein’s semantical views is the

difference between the naturalistic and the artifactual philosophies of the

semantics of language.

Semantical Revision and Heisenberg’s Doctrine of Closed-off Theories

Heisenberg called quantum theory “closed”, while Einstein in contrast

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said it is “incomplete”. An earlier and a later version of Heisenberg’s

semantical doctrine of “closed-off theories” may be distinguished. The

earlier version is given in his “Questions of Principle in Modern Physics”

originally given as a lecture at the University of Vienna in 1935 and since

published in his Philosophical Problems of Quantum Physics, where he sets

forth the central questions that are addressed by his philosophy of physics.

He firstly asks how it is possible for there to have occurred the strange

revision of the fundamental concepts of physics during the preceding thirty

years. Then secondly he asks what is the truth content of classical physics

and of modern physics in view of this conceptual revision. He notes that

these are also the questions that were posed and discussed by Bohr, who

approached them from the fundamental premises of quantum theory. It is

noteworthy that Heisenberg’s philosophy of science addresses questions

formulated by Bohr. The formulation of the questions in terms of how a

conceptual revision is possible suggests a naturalistic philosophy of the

semantics of language as a point of departure, since on the artifactual thesis

the possibility of a fundamental semantical revision is not problematic. When

concepts and meanings are understood to be cultural artifacts, then semantical

change may be expected as a matter of course.

As it happens, in his doctrine of closed-off theories Heisenberg did not

depart very far from the naturalistic thesis. He developed a theory of

semantical revision, but it is also a theory of semantical permanence.

Heisenberg has an earlier and a later version of his doctrine of closed-off

theories. In the earlier 1935 version he maintains that classical physics is

permanently valid, and that its concepts are necessary for experimentation in

physics. He states that classical physics is based on a system of

mathematically concise axioms, whose physical content is fixed by the choice

of words used in them. These words determine unequivocally the application

of the system of axioms to nature. Wherever concepts like mass, velocity and

force can be applied, there Newton’s law, F=ma, will be true. The validity

of the claim of this law is comparable to Archimedes law of the simple lever,

which today forms the theoretical basis for all load-raising machines, and

which will be true for all time. Therefore in spite of the fact that there has

been a revision of mechanics, the axiomatic system developed by Newton is

still valid. The revision pertains to the limits encountered in the application of

the axiomatized system of concepts of classical physics; it is not the validity

but only the applicability of classical laws that has come to be restricted by

relativity theory and quantum theory.

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Having thus described how he believes that the axiomatized

mathematical system of classical physics is permanently valid, Heisenberg

then describes how revision is possible. The revision of classical physics is

possible due to a “lack of precision” in the concepts used in the system.

While the quantitative variables x, t, and m used in the Newtonian system are

linked without ambiguity by the system of equations, which contain no degree

of freedom apart from initial conditions, the words “space”, “time”, and

“mass”, which are attributed to those quantities are tainted with all the lack of

precision that may be found in their everyday use. The validity of classical

physics is limited by the lack of precision of the concepts contained in its

axioms. As a result of this lack of precision science may be forced into a

revision of its concepts as soon as it leaves the field of common experience;

the concepts currently used may lose their value for the orderly presentation

of new experience. But this revision cannot be known in advance.

He notes for example that before the experiences of quantum theory the

results of the Wilson cloud chamber experiments could unhesitatingly be

expressed as “we see in the cloud chamber that the electron has described

such and such a path”, and this simple description could be accepted as an

experimental fact. It was only later that physicists came to know from other

experiments the problematic nature of the phrase “path of an electron”.

Scientific progress consists initially in the unhesitating use of existing terms

for the description of experience, and then subsequently in the revision of

those terms as demanded by new experience. The lack of precision

contained in the systems of concepts of classical physics is necessary, and

therefore even the mathematically exact sections of physics represent only

tentative efforts to find our way among a wealth of phenomena.

Central to the doctrine of closed-off theories is the thesis that classical

concepts must be retained for experimentation in physics. So far as the

concepts of space, velocity and mass can be applied unhesitatingly, as in

everyday experiences, Newtonian principles still apply. The Newtonian laws

represent an “idealization” achieved by taking into account only those parts

of experience that can be ordered by the concepts of space, time and mass on

the assumption of objective events in time and space. Therefore they always

remain the basis for any exact and objective science. Since we demand of the

results of science that they can be objectively demonstrated, we are forced to

express these results in the language of classical physics. For example for an

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understanding of relativity theory, it is necessary to stress that the validity of

Euclidian geometry is presupposed in the instruments that are used to show

the deviation from Euclidian geometry, i.e., the measure of the deviation of

light (an apparent reference to Eddington’s 1919-eclipse experiment to test

relativity theory). Furthermore the very methods used for the manufacture of

these instruments enforce the validity of Euclid’s geometry for these

instruments within the range of their accuracy. Similarly we must be able to

speak without hesitation of objective events in time and space in any

discussion of experiments in atomic physics. Heisenberg concludes that

while the laws of classical physics seen in the light of modern physics appear

only as limiting cases of more general and abstract connections, the concepts

associated with these laws remain an indispensable part of the language of

science, without which it is not possible even to speak of scientific results.

Therefore, while mathematically exact sections of classical physics are

tentative, the classical concepts must nevertheless be used for the description

of experiments.

Heisenberg offers a later version of his doctrine of closed-off theories

in several later articles and chapters in his books. In his earlier version

meanings found in everyday words, which are associated with variables in

mathematically expressed axiomatic systems of physical theories, retain their

vagueness in Newtonian physical theory. In his later version association of

the vague everyday meanings with the terms in the axiomatic system resolves

their vagueness, because the axiomatic systems have a definitional function.

This development represents his transition to context-determined relativized

semantics, where the relevant context is the axiomatic system of a physical

theory.

In “The Notion of a ‘Closed Theory’ in Modern Science” in Across the

Frontiers he discusses the criteria for scientific criticism and the evolution of

the aim of science. He writes that when Einstein developed his special theory

of relativity, it was evident that Maxwell’s theory of electromagnetic

phenomena could not be traced back to mechanical processes that obey

Newton’s laws, and the inference seemed unavoidable that either Newtonian

mechanics or Maxwell’s theory must be false. Physicists concluded that

Newton’s theory is strictly speaking false. This mislead many scientists into

unwittingly attempting to describe the phenomena of the world exclusively by

means of the concepts of field theory. This represented an aim of science that

is commonly accepted from Newton’s theory that science should proceed by

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means of a unitary conceptual scheme, except that now the concepts should

be those of field theory instead of classical mechanics.

But in both cases the concepts supplied an objective and causal

description of the process involved, and were therefore thought to be

universal. These common concepts were rejected by quantum theory for the

description of the atom, although they must still be used to describe the

results of an observation while standing in a complementary relation to one

another. Thus Heisenberg concludes that physicists no longer say that

Newton mechanics is false and must be replaced by quantum mechanics

which is correct. Instead they say that classical mechanics is a consistent self

enclosed scientific theory, and that it is a strictly true and correct description

of nature, whenever its concepts can be applied. Quantum theory has only

restricted the applicability of Newtonian mechanics, and has made classical

physics a “closed-off” theory. Heisenberg says that in contemporary physics

there are four great disciplines that have closed-off theories. They are firstly

Newtonian mechanics, secondly Maxwell’s theory and special relativity,

thirdly the theory of heat and statistical mechanics, and fourthly

nonrelativistic quantum mechanics, atomic physics and chemistry. General

relativity is not yet closed off.

Heisenberg then turns to a discussion of the properties of a closed-off

theory and of its truth content. A closed-off theory is consistent as an

axiomatized mathematical system. The most celebrated example is Newton’s

Principia Mathematica. And the concepts of the theory must be directly

anchored in experience. Before the axiomatic system is developed, concepts

describing everyday life remain firmly linked to the phenomena and change

with them; they are compliant toward nature. But when they are axiomatized,

they become rigid, and they “detach” themselves from experience. This is the

distinctive aspect of his later version of the doctrine of closed-off theories.

The system of concepts rendered precise by axioms is still very well adapted

to a wide range of experiences, but axiomitization of concepts sets a decisive

limit to their field of application. The discovery of these limits is part of the

development of physics. Yet even when the boundaries of the closed theory

have been encountered and overstepped, and when new areas of experience

are ordered by means of new concepts, the conceptual scheme of the closed

theory still forms an indispensable part of the language in which the physicist

speaks of nature. The closed theory is among the presuppositions of the

wider inquiry; we can express the result of an experiment only in the concepts

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of earlier closed theories. Heisenberg summarizes the properties of closed-

off theories as follows: Firstly the closed-off theory holds true for all time.

Whenever experience can be described by the concepts of the closed-off

theory, even in the most distant future, the laws of this theory will always be

correct. Secondly the closed-off theory contains no perfectly certain

statements about the world of experiences; its successes are contingent.

Thirdly even with the indeterminacy of its contingency, the closed-off theory

remains a part of scientific language, and therefore is an integrating

constituent of our current understanding of the world.

Heisenberg sees the evolution of modern science differently than

Einstein’s description in “Physics and Reality”. Heisenberg says the

historical process that gave rise to the whole of modern physics since the

conclusion of the Middle Ages, consists in a succession of intellectual

constructs, which take shape as if from a “crystal nucleus”, out of individual

queries raised out of experience, and which eventually once the complete

crystal has developed, again detach themselves from experience as purely

intellectual structures that forever illuminate the world for us as closed-off

theories. Thus the history of science is like the history of art, where the goal

is to illuminate the world by means of intellectual constructs. In his “The End

of Physics” in Across the Frontiers he adds that while physics consist of

many closed-off systems, it is not possible to close off physics as a whole.

Today it is necessary to seek out new and still more comprehensive closed-

off theories or “idealizations” as he also calls them, which will include both

relativity theory and quantum theory as limiting cases.

Closely related to his thesis of closed-off theories is Heisenberg’s

theory of abstraction. In “Abstraction in Modern Science” in Across the

Frontiers he defines abstraction as the consideration of an object or a group

of objects under one viewpoint while disregarding all other properties of the

object. All concept formation depends on abstraction, since it presupposes

the ability to recognize similarities. Primitive mathematics developed from

abstraction, e.g., the concept of the number three. Mathematics has formed

new and more comprehensive concepts, and thereby ascended to ever higher

levels of abstraction. The realm of numbers was extended to include the

irrational and complex numbers. This view is quite different from Bohr’s,

who believed that the mathematical formalisms used in physics have no

descriptive semantical value but are merely symbolic, i.e., semantically

vacuous, instruments for calculation and prediction, particularly if they

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contain complex numbers or represent more than four dimensions as in

quantum theory. In Heisenberg’s philosophy abstraction, the consideration of

the real from a selective viewpoint, produces idealizations of reality which are

axiomatic mathematical structures that become closed-off, as the historical

development of science reveals the limitations of their applicability and

occasions the creation of new theories.

In expounding his semantical doctrine of closed-off theories

Heisenberg departed from Bohr. Comparison of their views reveals essential

similarities, but it also reveals differences. Bohr’s semantical views are

stated in “Discussions with Einstein” where he says that Planck’s discovery

of the quantum of action makes classical physics an “idealization” that can be

unambiguously applied only in the limit, where all actions involved are large

in comparison with the quantum. A more elaborate statement is given in

“The Solvay Meetings” in Essays 1958/1962. There he firstly says that

unambiguous communication of physical evidence demands that the

experimental arrangement and the reading of observations be expressed in

common language suitably refined by the vocabulary of classical physics.

Then secondly he states that in all experimentation this demand is fulfilled by

using as measuring instruments bodies like diaphragms, lenses, and

photographic plates, which are so large and heavy that notwithstanding the

decisive rôle of the quantum for stability and properties of such bodies, all

quantum effects can be disregarded in the account of their position and

motion. Finally and thirdly he says that in classical physics we are dealing

with an idealization according to which all phenomena can be arbitrarily

subdivided, and all interaction between measuring instruments and the object

under investigation can be neglected or compensated for. Bohr seems to be

using the term “idealization” as Heisenberg does, but he reserves it for the

classical physics. Bohr does not admit a separate set of distinctively quantum

concepts, because he maintains an instrumentalist interpretation of the

quantum theory mathematical formalism. In his view there are no quantum

concepts defined by the equations of the quantum theory, but rather there are

only classical concepts, while the semantically uninterpreted mathematical

formalism generates predictions expressed in classical terms.

Bohr’s “Forms of Perception” and Neo-Kantianism

Having based his doctrine of closed-off theories on Bohr’s philosophy

of observation, Heisenberg attempted to relate Bohr’s philosophy to the

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history of philosophy, and specifically to Kantianism. Heisenberg’s

statements are found in his “Recent Changes in the Foundations of Exact

Science” (1934) in Philosophical Problems of Quantum Physics, in his “The

Development of Philosophical Ideas Since Descartes in Comparison with the

New Situation in Quantum Theory” in Physics and Philosophy, in his

“Quantum Physics and Kantian Philosophy (1930-1932)” in Physics and

Beyond, and in his “Planck’s Discovery and the Philosophical Problems of

Atomic Theory” in Across the Frontiers. Like Einstein, Heisenberg rejects

the positivist phenomenalism and advocates realism; he was never a

metaphysical Idealist, Kantian or otherwise. In “Planck’s Discovery” he

states that quantum theory does not consider sense impressions to be the

primary given, and that if anything is the primary given in quantum theory, it

is the reality described with the concepts of classical physics. And in

“Development of Philosophical Ideas Since Descartes” he describes his

realistic variation on Kant’s views with the phrase “practical realism”, since

in Heisenberg’s view things rather than perceptions are the given for the

human mind.

But while Heisenberg is opposed to positivism as much as Einstein, his

referencing the philosophy of Kant is not motivated by his antipositivism.

Heisenberg is interested merely in relating Kantianism to the philosophy of

observation he took from Bohr and incorporated in his doctrine of closed-off

theories. In “Recent Changes in the Foundations of Exact Science” he says

that in the field of philosophy of perception, Kant’s philosophy has been put

into a new light as a result of the critique of absolute time and Euclidian space

by relativity theory and by the critique of the law of causality by quantum

theory, and that the question of the priority of the forms of perception and of

the categories of the understanding must be reconsidered. He states that there

are two apparently contradictory propositions that must be reconciled: On the

one hand relativity theory and quantum theory have shown that our space-

time forms of perception and the category of causality are not independent of

all experience in the sense that they must for all time remain essential

constituents of every physical theory. On the other hand, as Bohr taught, the

applicability of the classical (i.e., Kantian) forms of perception and the law of

causality are the premises of every objective experience even for modern

physics. The physicist can only communicate the course of an experiment

and the result of a measurement by describing the necessary manual

operations and instrument readings as objective events taking place in the

space and time known to our intuition. And he could not infer the properties

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of the observed object from the result of measurement, unless the law of

causality guaranteed an unambiguous connection between measurement and

object. Heisenberg resolves the contradiction between the two statements as

follows: Physical theories can have a structure differing from classical

physics, only when their aims are no longer those of immediate sense

perception; that is to say, only when they leave the field of common

experience dominated by classical physics.

In “Quantum Physics and Kantian Philosophy” Heisenberg views

Kant’s philosophy of perception as a closed-off theory, as he elsewhere

describes closed-off theories in physics. He compares the validity of Kant’s

philosophy to the validity of Archimedes’ theory of the lever, and he states

that Kant’s theory is eternally true, just as Archimedes’ theory is eternally

true. Kant’s analysis of perception represents true knowledge that applies

wherever thinking beings enter into the kind of contact with their environment

called “experience”. Relativity theory and quantum theory have defined the

limits of the a priori in the exact sciences in ways that could not have been

known to Kant. The a priori has not been eliminated from physics, and

Kant’s analysis of how we come by our experiences is essentially correct.

But the a priori has become “relativised” in the sense that classical concepts

are a priori conditions for relativity and quantum theory, since classical

concepts are necessary for experiments. Remarkably Heisenberg says that

the progress of science has changed the structure of human thought, and has

taught us the meaning of “understanding”. In the closing paragraph of his

“Quantum Physics and Kantian Philosophy” Heisenberg states that he has

described the relationship between Kant’s philosophy and modern physics

from the perspective of Bohr’s teachings.

On Scientific Revolutions

Heisenberg considers the development of modern quantum theory to be

one of the two great scientific revolutions in twentieth century physics; the

other in his view is relativity theory. Few would disagree. The complete title

of his 1958 book is Physics and Philosophy: The Revolution in Modern

Science. But by the 1960’s the term “revolution” as used in connection with

the development of science had become what Heisenberg calls a “vogue

word” due to some similarities between scientific revolutions and social

revolutions. Possibly the vogue status of the term is due in part to the popular

monograph, Structure of Scientific Revolutions, written by Thomas Kuhn in

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the United States in 1962, but Heisenberg never references Kuhn, and their

views are not the same. Heisenberg discusses his idea of revolution in

science in a lecture delivered to the Association of German Scientists in

Munich in 1969, which was published in English in 1974 as “Changes of

Thought Pattern in the Progress of Science” in his Across the Frontiers.

Heisenberg recognizes the operation of sociological forces in the scientific

professions, but his views are different from those of Kuhn.

Heisenberg defines a “revolution” in science as a change in thought

pattern, which is to say a semantical change. He states that a change in

thought pattern becomes apparent, when words acquire meanings that are

different from those they had formerly, and when new questions are asked.

He does not reference his semantical thesis of closed-off theories in this

context, although the episodes in the history of post-Newtonian physics that

he cites as examples of scientific revolutions are the same as those that he

also says resulted in new closed-off theories in the history of physics. And

the semantical change that occurs in the transition to a new axiomatic theory

and the closing off of the old one, is the change involved in the transition to a

new thought pattern. The central question that Heisenberg brings to the

phenomenon of revolution in science understood as a change in thought

pattern, is how the revolution is able to come about. The occurrence of the

revolution is problematic due to resistance to the change in thought pattern

offered by the cognizant profession. Heisenberg also expresses the question

in more sociological terms, when he asks how a small group of physicists are

able to “constrain” other physicists to make the change in thought pattern in

spite of the latter’s resistance to do so. Firstly he discusses the reasons for

resistance. Then he discusses various proposed explanations about how the

resistance is overcome.

In his discussion of the reasons for resistance he states that there have

always arisen strong resistances to every change in the pattern of thought.

The progress of science proceeds as a rule without much resistance or

dispute; the scientist has by training been put in readiness to fill his mind with

new ideas. But the case is altered when new groups of phenomena compel

changes in the pattern of thought. Here even the most eminent of physicists

find immense difficulties, because a demand for change in thought pattern

may create the perception that the ground is to be pulled from under one’s

feet. A researcher who has achieved great success in his science with a

pattern of thinking he has accepted from his young days, cannot be ready to

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change this pattern simply on the basis of a few novel experiments.

Heisenberg states that once one has observed the desperation with which

clever and conciliatory men of science react to the demand for a change in the

pattern of thought, one can only be amazed that such revolutions in science

have actually been possible at all. Undoubtedly the case in Heisenberg’s

experience is the desperation that he saw in Schrödinger’s and especially

Einstein’s opposition to the new thought pattern represented by the

Copenhagen interpretation of the quantum mechanics.

He then considers several possible answers to the question of how

scientific revolutions can come about in spite of the resistances, of how the

resistances are overcome. One answer that he rejects is that the revolution is

due to a strong revolutionary personality. He maintains that no such strong

personality could overcome the profession’s resistance. Another answer that

he rejects might be described as a variation on the conspiracy thesis, the view

that a small group of physicists intended from the outset to overthrow the

existing state of the science. He states that never in its history has there ever

been a desire for any radical reconstruction of the edifice of physics; this is

because at the onset of a revolution there is a very special, narrowly restricted

problem, which can find no solution within the traditional framework. The

revolution is brought about by researchers who are genuinely trying to resolve

the special problem, but who otherwise wish to change as little as possible in

the previously existing physics. It is precisely the wish to change things as

little as possible, which demonstrates in Heisenberg’s opinion that the

introduction of novelty is a matter of being compelled by the facts. The

change of thought pattern is imposed by the phenomena. He concludes

therefore that the way to make a scientific revolution is to try to change as

little as possible: it is an error to demand the overthrow of everything existing

due to the risk of attempting a change that nature makes impossible. Small

changes on the other hand show what is compelled by the facts, and in the

course of years or decades enforce a change in thought pattern and shift the

foundation of the science. The relevant example of such a small change is

Planck’s quantum of action, which years later resulted in the modern quantum

theory.

Having rejected the view that scientific revolution occurs due to a

conspiracy either with or without a strong revolutionary personality,

Heisenberg then considers the answer that the resistances to revolution are

overcome simply because there is a “right” and a “wrong” in physics, and the

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new theory is right while the old theory is wrong. It is noteworthy that

Heisenberg does not reject the thesis that there is a right and a wrong in the

sense of a correct and an incorrect, and in view of his thesis of closed-off

theories, it would be remarkable if he did. Furthermore he had explicitly

rejected historical relativism in his “Quantum Physics and Kantian

Philosophy”. Still he finds that there is a problem with this answer as an

explanation for overcoming resistances, namely that historically the right

theory has not always prevailed. He cites as an example the dominance of the

geocentric theory of Ptolemy over the heliocentric theory of Aristarchus, who

lived in the third century BC.

Therefore, while there are absolute standards for criticism of scientific

theories, there still remains the question of why some correct theories succeed

in gaining acceptance over the strong forces of resistance, while others do

not, even though the rejected theories may be correct. Heisenberg then

proposes his own answer. Scientists perceive that with the new pattern of

thought, they can achieve greater success in their science than with the old;

the new system proves to be more fruitful. Heisenberg states that once

anyone has decided to be a scientist, he wants above all to get ahead, to be on

hand when the new roads open up; it does not satisfy him merely to repeat

what is old and has often been said before. Consequently the scientist will be

interested in the kind of problems where there is something to be done, where

he has the prospect of successful work. That is how relativity theory and

quantum theory came to prevail according to Heisenberg. He describes this

as a “pragmatic criterion of value”, and he states that while one cannot

always be certain that the right theory will always prevail, nevertheless these

are forces that are strong enough to overcome the resistances to a change in

thought pattern.

Since Heisenberg is a principal participant in one of the great scientific

revolutions in modern physics, his views based on his personal experience

deserve singular consideration. He was undoubtedly impressed by the

resistances offered to the Copenhagen interpretation by Schrödinger and

especially by Einstein. While few contemporary philosophers of science

accept Heisenberg’s doctrine of closed-off theories with its naturalistic view

of observation, which he uses to interpret his experience of scientific

revolution, they recognize the operation of sociological forces including the

thrust of opportunistic careerism. And they also recognize that semantical

change occurs in scientific revolutions, and that the adjustment it imposes on

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the affected profession operates as a cause of resistance within it, even

though they do not accept Heisenberg’s theory of semantical change and

permanence. Unlike others such as Kuhn, Heisenberg does not identify the

institutionalized criteria for scientific criticism with the existing thought

pattern, and he does not maintain that the revolution is a change with no

institutional framework controlling it. Heisenberg avoids the historical

relativism found by many in Kuhn’s thesis, and which is explicitly embraced

by Feyerabend. And one would not expect the proponent of the doctrine of

closed-off theories and the advocate of Bohr’s theory of observation to find

the process of scientific criticism very problematic. The scientist is simply

compelled by the facts, and the semantics of the statements of fact are not a

problematic matter. Failure of the correct theory to overcome the forces of

resistance, and indeed the very existence of those resistances, is due to the

professional failure of those who cannot adjust to new thought patterns when

the facts compel, and not to any inherently problematic character in the

process of scientific criticism itself.

One can only wonder what Heisenberg might have said, were he to

have followed through with Einstein’s thesis that it is the theory that decides

what the physicist can observe; how he would have addressed the consequent

problem that the concepts used to describe the facts are supplied by the

choice of thought patterns expressed in the new theory.

Heisenberg’s Philosophy of Science

Heisenberg’s rich and extensive philosophical writings can be related

to the four functions performed in basic-scientific research:

Aim of Science

The aim of science has a special importance in Heisenberg’s

philosophy, because it was explicitly developed to defend the Copenhagen

interpretation of quantum theory against Einstein’s explicitly formulated

programmatic aim of all physics. Heisenberg’s views are expressed in his

“Notion of ‘Closed Theory’ in Modern Science” and in his “On the Unity of

the Scientific Outlook on Nature” (1941) in Philosophical Problems of

Quantum Physics. Einstein used his programmatic aim of physics to claim

that the statistical quantum theory is “incomplete” in the sense that it does not

represent an adequate explanation for the problem that it addresses, and that

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further research work is still needed. The reason he said it is still incomplete

is that it is not consistent with the ontology of field physics, which describes

physical reality as continuous in four dimensions and deterministic.

But Heisenberg denied Einstein’s contention that the microphysical

theory must employ the same ontological concepts as those used in

macrophysical field theory, and his doctrine of closed-off theories was

motivated by his desire to show how multiple ontologies can co-exist in

physics. This is Heisenberg’s thesis of pluralism in science. The

Copenhagen interpretation of quantum theory is complete in Heisenberg’s

view, because it is a closed-off theory. And like all closed-off theories it is

not only a complete solution to the problem that it addresses, but it is also a

permanently true solution. In Heisenberg’s philosophy the aim of science is

to progress through a sequence of closed-off theories, and it is not, as

Einstein maintained, to progress toward a single and all-inclusive ontology.

The result of physics pursuing its aim as Heisenberg views it, has been his

architectonic scheme for physics, a scheme of closed-off theories which he

delineates in his “Relation of Quantum Theory to Other Parts of Natural

Science” in Physics and Philosophy.

Scientific Discovery

In Heisenberg’s treatment of scientific discovery two aspects may be

distinguished: One is the syntactical or structural aspect, and the other is the

semantical or the interpretative aspect that also implies ontological

considerations. The structural aspect pertains to the development of the new

mathematical theory. The new quantum theory formal structure was the result

of repeated failures of conservative attempts by the researchers to extend the

classical theory, in order to explain phenomena at the microphysical order of

magnitude. But eventually research resulted in the revolutionary development

that is quantum mechanics.

Closely related to the first aspect is the second, the interpretative

problem. When extension of Newtonian physics could not solve the problem

of microphysics, and after Heisenberg eventually developed the matrix

mechanics, the semantical and ontological interpretation of the new matrix

mechanics still remained problematic. Using Einstein’s thesis that the theory

decides what the physicist can observe, Heisenberg reinterpreted the

observed tracks in the Wilson cloud chamber experiment, and developed the

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indeterminacy relation with its nondeterministic and duality ontology. The

new interpretation was accomplished by taking the new quantum theory

realistically, as a description of the ontology of the microphysical world.

When Einstein attacked the statistical quantum theory, he attacked only the

second aspect, the Copenhagen interpretation with its nondeterministic

ontological claim; he rejected indeterminacy as a valid ontological claim.

Scientific Explanation

Heisenberg’s views on the issue of scientific explanation are implicit in

his position against Einstein’s objections to the Copenhagen interpretation.

Einstein’s objection to the Copenhagen interpretation is that it is incomplete

as a scientific explanation. This objection is a very traditional type of

objection, because historically the concept of scientific explanation has been

defined in terms of one or another ontology, and Einstein demanded

conformity to the ontology defined by the concepts in Newtonian and field

physics. Bohr placed himself and his Copenhagen colleagues at a

disadvantage, when he employed the vocabulary of their critics by referring to

the statistical quantum theory as “noncausal”, because he accepted the

definition of causality in terms of the deterministic ontology of classical

physics and field theory.

But Heisenberg also maintained that the revolutionary developments in

physics include interpreting the new mathematical formalism realistically. He

saw this in Einstein who accepted the field as real, accepted relativistic time

as real time, and abandoned the concept of absolute time. Invoking Einstein’s

practice as his precedent, Heisenberg likewise accepted his indeterminacy

relation as describing the real microphysical world as nondeterministic. This

amounts to separating the concept of scientific explanation from any

preconceived ontology. Such separation had occurred previously in the

history of physics, but its recognition was quite radical in microphysics after

the lengthy domination of Newtonian physics, even though it is now the

common property of the contemporary pragmatist philosophers of science in

their thesis of ontological relativity.

Scientific Criticism

In striking contrast to his radical concept of scientific explanation,

Heisenberg’s treatment of the question of scientific criticism is very

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conservative. Actually it is anachronistic, because he believed that his

doctrine of closed-off theories enables him to explain how scientific theories

can be permanently true. His views of explanation and of criticism represent

a very unusual combination of views. Historically philosophers and scientists

have maintained that scientific explanations are permanently true, because as

explanations they purport to describe correctly the one and only true

ontology. Heisenberg’s philosophy of scientific criticism includes a

semantical thesis, which is a thesis of both semantical change and semantical

permanence. Whether or not this semantical thesis is a sustainable one is

certainly questionable, particularly when it depends on such curious processes

as the semantics of words becoming “detached” from the variables occurring

in the closed-off axiomatic theories, when the theories encounter the limits of

their applicability.

A philosopher of science such as Popper would dismiss such a thesis

as a “content-decreasing” stratagem. If when a theory is criticized by an

experimental test, the words expressing the test outcome describe something

contrary to what the theory had predicted, then a later attempt to save its truth

claim by equivocation, by the “detachment” of the meanings describing the

experimental outcome from the terms in the theory, only makes the theory

tautological. In other words Heisenberg’s doctrine in effect says a theory is

true where it is true, and that where it is not true, it is not falsified, because it

becomes silent, detached and inapplicable

Comment and Conclusion

In “Bohm and the ‘Inevitability’ of Acausality” in Bohmian Mechanics

and Quantum Theory: An Appraisal (1996) Mara Beler takes a cynical

perspective to Heisenberg’s inconsistency, arguing that he had neither belief

nor commitment, but only a selective and opportunistic use of Bohrian

doctrine for the finality of the Copenhagen orthodoxy. Such might be the

appearances, but Heisenberg was not cynical. A new philosophy does not

spring forth as from the brow of Zeus – coherent, complete, and finally

formed. It struggles to emerge from the confusion produced by the inevitable

conflict between new seminal insights and old conventional concepts. It is not

surprising, therefore, that there should exist an inconsistency between the

seminal insights in Heisenberg’s philosophical reflections described in his

autobiographical accounts, and the conventional concepts in his systematic

philosophy of science described in his doctrine of closed-off theories.

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Naturalistic vs Artifactual Semantics for Observation Language

There is indeed an inconsistency in Heisenberg’s philosophy, and it is

due to the conflicting influences of Bohr and Einstein. The conflict has its

basis in two fundamentally different philosophies of the semantics of

language; particularly where the relevant language is the vocabulary used to

conceptualize the sense stimuli delivered in observations. The philosophy of

language in contemporary pragmatist philosophy of science is the artifactual

thesis of semantics, and the traditional philosophy is the naturalistic thesis.

Bohr’s naturalistic philosophy of language is that the semantics of language is

the natural product of perception, such that concepts used for observation are

what in Atomic Theory and the Description of Nature he calls the “customary

forms of perception”, which have their information content determined by

nature and the natural processes of perception, and which therefore relegate

the mathematical quantum theory to instrumentalist status. Einstein’s

artifactual philosophy of language on the other hand is that the semantics of

language is an artifact, a “free convention”, a cultural product instead of a

natural product, such that concepts and categories used for observation in

physics do not have their information content specifically determined by the

natural processes of perception, and are therefore changeable.

It was evident to Heisenberg as well as to every other physicist at the

time that revolutionary revisions had been made in twentieth-century physics.

Heisenberg wanted to explain how such developments in the history of

science could produce correspondingly revolutionary revisions in the

semantics of the language of physical theory. Heisenberg’s response was his

doctrine of closed-off theories, and the philosophy of language that he used

for this semantical theory was due to the influence of Niels Bohr. This

doctrine restricts semantical revision to the description of phenomena that lie

beyond ordinary perception, and thereby retains semantical permanence for

the description of phenomena accessible to ordinary observation and

described by the language and concepts of Newtonian physics. According to

Heisenberg’s doctrine of closed-off theories Newtonian physics is

permanently valid and serves as the observation language for physics,

because it is necessary for reporting experimental measurements and other

observations.

Thus Heisenberg believed that all observation must be with concepts

supplied by either classical physics or “everyday” language. In his mature

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version of his doctrine of closed-off theories these concepts are not the same.

The everyday concepts have a “lack of precision” or vagueness, while the

concepts of classical physics have their semantics rigidly and precisely

defined by the context consisting of the laws of Newtonian physics. The

concepts of quantum physics also have their content fixed by the context

consisting of the laws of quantum physics. What is significant is that the laws

of classical and quantum physics are mutually inconsistent. And most notably

in Heisenberg’s view the quantum concepts are not merely alternative

resolutions of the vagueness in everyday concepts, but they cannot be used

for observation. The fact that classical and quantum concepts occur in

mutually inconsistent laws implies that, when these concepts are associated

with the same descriptive term or variable, they are alternative meanings

making that common term equivocal.

The equivocal relation between classical and quantum concepts is

illustrated in the cases of the terms “position” and “momentum”, which occur

in both classical and quantum physics. The advocates of the Copenhagen

interpretation of the quantum theory argue that in practice the concepts of

classical physics must operate in descriptions of the macrophysical

experimental apparatus and observation measurement. This classical

semantics includes the idea that nature is fundamentally continuous, and the

idea that in principle the measurements can be indefinitely accurate,

notwithstanding the fact that in practice the degree of accuracy is always lim-

ited. They also argue that there are meanings for these terms that are

distinctive of quantum physics, and this semantics, which is defined by the

context supplied by the indeterminacy relations, includes the ideas that nature

is fundamentally discontinuous and that the accuracy of the joint measurement

of momentum and position is limited by Planck’s constant. Therefore, on

Heisenberg’s philosophy of closed-off theories, in order for observation to be

possible in quantum physics there must exist an equivocation for every term

common to classical and quantum physics, such that for every quantum

concept determined by the context of quantum physics there must be a

corresponding classical concept for observation determined by the context of

classical physics. Such is the unfortunately equivocal outcome of

Heisenberg’s explicit and systematic philosophy of science.

Yet Heisenberg’s use of Einstein’s aphorism for describing the tracks

in the Wilson cloud chamber, which led to his subsequent development of the

indeterminacy relations, does not agree with the observation language

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required by his doctrine of closed-off theories. Einstein’s aphorism is the

semantical thesis that the theory decides what the physicist can observe,

and for microphysical experiments this thesis implies that the quantum

theory contributes to defining the semantics for observational

description.

The Contemporary Pragmatist Alternative

Contrary to Heisenberg’s semantical doctrine of closed-off theories,

classical concepts are not necessary for observation, variables in the quantum

laws are not equivocal, and all the concepts in the quantum theory are

quantum concepts that are operative in observational description. It is

possible with a metatheory of semantical description to follow through with

Einstein’s aphorism and to say that theory decides what the physicist can

observe, because the concepts used for observation are quantum concepts.

Such a new semantical theory is needed, because like Bohr, Heisenberg had

premised his doctrine of closed-off theories on the naturalistic philosophy of

language. Attempts to preserve a permanent semantics for observation, while

at the same time to explain the semantical revisions produced by the

revolutionary developments in theory, result in a positivist philosophy of

language that attributes equivocation to language that in practice physicists

are routinely able to use unambiguously. The historic twentieth-century

scientific revolutions have motivated post-positivist philosophers of science to

reject the naturalistic philosophy of the semantics of language, and to accept

the artifactual philosophy instead. It is necessary to consider further how to

describe the semantics both of quantum theory and of experimental

observation, in order to exhibit how concepts are culturally determined as

linguistic artifacts instead of predetermined as products of nature, and to

explain why semantical change occurs in observation reporting without

involving complete equivocation.

False Assumptions in Closed-off Theories Doctrine

Heisenberg’s doctrine of closed-off theories contains certain basic

assumptions that are in need of reconsideration. The first is the tacit

assumption that all concepts are indivisible or simple wholes, that must be

either completely different or completely the same, such that classical and

quantum concepts are simply and wholly equivocal. The second is the

explicit assumption that observation language must be exclusively

associated with macroscopic phenomena. Both of these assumptions

contain errors.

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Firstly it is incorrect to assume that the meanings of terms in physics

or in any other discourse are simple wholes that cannot be analyzed into

component parts. Secondly it is necessary to reconsider the Copenhagen

school’s basis for dividing the relevant language into statements of

experiment and statements of theory. Specifically rejection of the naturalistic

philosophy of language implies rejecting two mental associations that occur in

Heisenberg’s doctrine of closed-off theories. The first is the classical-

macroscopic-observation association, and the second is the quantum-

microscopic-theoretical association. Consider firstly the pragmatist

alternative to the wholistic view, and how it affects Heisenberg’s thesis of

equivocation.

Semantical Wholism Rejected

Conventional habitual meanings of words are synthetically experienced

wholistically. However reflection on the common occurrence of looking up

words like a common noun in a unilingual dictionary reveals that the

meanings of words are not simple wholes, but rather have component parts

that are identified by the defining words occurring in the dictionary definition

or lexical entry. Dictionary definitions that are not proper names give

semantical descriptions of the meanings they define, and in order to function

in this way they always must have the force of universally quantified

statements accepted as true. Furthermore dictionary definitions are often

viewed as describing the complete meaning of the term, but dictionary

definitions are actually minimal statements, and by no means give complete

meaning. Usually the understanding of the meaning of a univocal term,

especially a technical term, requires a larger context consisting of a discourse

having many statements containing the term. Today such larger context may

be examined extensively with the aid of a key-word-in-context computer

program.

Since Quine rejected the analytic-synthetic distinction, all universal

empirical or “synthetic” statements accepted as true may also be viewed as

definitional or “analytic”. Thus if one were to make a list of logically

consistent universally quantified affirmative categorical statements containing

a univocal descriptive term as their common subject term with each statement

accepted as true, then the predicates in each of the mutually consistent

statements constituting the list describe part of the meaning of the common

subject term, and the entire list as well as each statement in it may be called a

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“semantical description” of the univocal common subject term’s meaning. In

summary a semantical description consists of the language context, in

which a descriptive term’s meaning is determined and described by a set

of universal affirmations believed to be true.

This contextual determination of the semantics of language is the

essence of the artifactual thesis. Quine calls this context the “web of belief”.

A term is equivocal if any of the universal affirmations in the semantical

description are mutually inconsistent. This equivocation is made explicit,

when the predicates of the inconsistent universal affirmations can be related

to one another by universal negations accepted as true. The several different

meanings in the equivocation each have separate semantical descriptions,

which can be exhibited when the original list is subdivided into mutually

exclusive subsets with each subset containing only mutually consistent

universal affirmations. Then each subset is a semantical description of one of

the several different meanings of the equivocal term instead of each subset

functioning as a description of different parts of the one meaning of a

univocal term.

The equivocations postulated by Heisenberg’s doctrine of closed-off

theories as applied to microphysics are the result of the logical inconsistency

between the theories of classical and quantum physics. Thus there exists

equivocation with each theory context constituting a separate semantical

description list for any term common to the two theories, terms such as

“position” or “momentum”.

In addition to the properties of equivocation and univocation there is

another aspect of language called vagueness. Equivocation and univocation

are properties of terms, while vagueness and clarity are properties of

meanings. Meanings are more or less clear or vague. Two concepts are clear

in relation to one another, if they can be related to each other by universal

affirmations or negations accepted as true, and they are vague in relation to

each other if they cannot be so related by any universal statements. And

adding any universal affirmations or negations believed to be true to a single

univocal term’s semantical description list has the effect of reducing the

vagueness in the concept associated with the term by explicitly adding or

excluding meaning.

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Every meaning is always vague and admits to further clarifying

resolution, because potentially its semantical description can always be

increased by additional universal statements believed to be true. This

becomes evident when instances are encountered about which no decision

had been made regarding the applicability of the term in question. Friedrich

Waismann has called this inexhaustible residual vagueness the “open texture”

of concepts. What Heisenberg calls “everyday language” is merely language

which has a degree of vagueness or “lack of precision” that is greater than the

degree of vagueness in Newtonian and quantum concepts due to the latter’s

contexts consisting of their respective equations. However no terms that are

part of a language including everyday terms can be utterly without any

defining context such as is found in the term’s lexical entry in a dictionary.

Naturalistic “Observation” and “Theory” Rejected

Consider next the relation between the language of observation and the

language of theory, the second basic assumption in the doctrine of closed-off

theories. Scientists and philosophers still conventionally use the word

“theory” to refer to Newton’s “theory” of gravitation, to Einstein’s “theory”

of relativity, and to the quantum “theory”, even though the physics profession

had decided many years ago either to accept or to reject these expressions as

physical laws and explanations. As Norwood Russell Hanson, Yale

University pragmatist philosopher of science and advocate of the Copenhagen

interpretation of quantum mechanics, notes in this conventional usage the

term “theory” does not function as it did when these expressions were firstly

advanced for testing as proposed explanations of problematic phenomena in

research science. When they were firstly proposed, these expressions

represented statements that had a much more hypothetical status in the

judgment of the cognizant professions than they do today, and they were

typically topics of controversy.

There is, therefore, an ambiguity between “theory” understood as an

accepted or rejected explanation in what Hanson called “catalogue science”,

and “theory” understood as a tentative proposal submitted for empirical

testing in what he called “research science”. In the “Introduction” to his

pioneering Patterns of Discovery: An Inquiry into the Conceptual

Foundations of Science (1958), Hanson wrote that earlier philosophers of

science had mistakenly regarded as paradigms of inquiry finished systems like

planetary mechanics instead of the unsettled, dynamic research sciences like

contemporary microphysics. He explains that the finished systems are no

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longer research sciences, although they were at one time. He therefore says

that distinctions applying to the finished systems ought to be suspect when

transferred to research disciplines, and that such distinctions afford an

artificial account of the activities in which Kepler, Galileo and Newton were

actually engaged. He thus maintains that ideas such as theory, hypothesis,

law, causality and principle, if drawn from what he calls the finished

“catalogue-sciences” found in undergraduate textbooks, will ill prepare one

for understanding research-science.

Only the functional meanings as found in what Hanson calls “research

science” are strategic in the contemporary pragmatist philosophy of science,

even though the conventional or “almanac” meaning of “theory” occurs even

in its own expository discourse such as herein. From this functional view

theory language that has been tested and not falsified by a decisive test ceases

to be a theory and has thereby been given the status of a law that can be used

in an explanation. Due to empirical underdetermination there may

nonetheless be multiple tested and nonfalsified former theories that address

the same problem, and that therefore also have the status of explanations

accepted by some scientists in the same profession. Some scientists are

uncomfortable with this pluralism, but the contemporary pragmatist

philosophers recognize such pluralism as historically characteristic of science.

In an empirical test of a theory the semantics of the vocabulary in all

the relevant discourse is controlled by a strategic decision that is antecedent

to the performance of the test. This is the functional decision as to what

statements are presumed for testing and what statements are proposed for

testing. The former language is the explicit statements of test design together

with usually many tacit assumptions. The latter language is the explicit

statements of the theory. This decision is entirely pragmatic, since it is not

based on the syntactical or the semantical characteristics of language, but

rather is based on the use or function of the language in basic research,

namely empirical testing. The test-design statements are those that by prior

decision and agreement among cognizant members of the profession have the

status of definitions. These statements are presumed to be true regardless of

the outcome of the test, and serve to identify the subject of investigation and

to describe the test execution procedure throughout the test. The theory is the

language that by prior decision and agreement among the cognizant members

of the profession has the less certain status of a hypothesis. The hypothesis is

believed to be true to the extent that it is considered worthy of testing,

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although the developer and his entourage of cheerleading advocates may be

quite firmly convinced. But if the test outcome is a falsification, then by prior

agreement among scientists who accept the test design, it is the statements of

theory and not the statements of test design that are judged to have been

falsified and in need of revision.

However, a falsification may lead some interested scientists, such as

the theory’s developer and advocates, to reconsider the beliefs underlying the

test design, even while admitting that the test was executed in accordance

with its design. This is a rôle reversal between test design and theory, which

may result in productive research. In such cases when the falsified theory is

made a test-design statement characterizing the problematic phenomenon, the

problem has become reconceptualized. As James Conant recognized to his

dismay in his On Understanding Science: An Historical Approach, the

history of science is replete with such prejudicial responses to scientific

evidence that have nevertheless been productive and strategic to the

advancement of basic science in historically important episodes.

The decision distinguishing test-design language and theory language

made prior to the experiment may but need not result in identifying

mathematical equations as the statements of theory and of identifying

colloquial discourse as the statements of test design. The decision is not

based on syntactical characteristics of the language, and the test-design

statements often include mathematically expressed statements together with

statements in colloquial language describing the measured phenomenon, the

measurement procedures, and the design and operation of the measurement

apparatus. Even more relevantly the decision is not based on semantical

criteria, as advocates of the naturalistic philosophy of the semantics of

language believe. Contrary to both Bohr and the positivists the decision is

not based on any purportedly inherent distinction between observation and

theory, whether or not, as in the case of quantum mechanics, the observation

concepts are called “classical” or “macroscopic”, and the theoretical concepts

are called “quantum” or “microscopic”. The distinction between statements

of test design and statements of theory is neither syntactical nor semantical; it

is distinctively and entirely pragmatic.

Test Language Before Test Execution

With the above concepts in mind and at the expense of some repetition

consider the language of an empirical test before the test is executed and its

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outcome is known. In order for the test-design statements to characterize

evidence independently of the theory proposed for testing, the test-design

statements and the theory statements must be logically independent; i.e.,

neither set of statements may be merely a logical or mathematical

transformation of the other. The test-design statements, the language

presumed for testing, may neither deductively imply nor contradict the theory

or any of its alternatives. In the case of quantum mechanics this means that

the test-design language for experiments cannot be from Newtonian physics,

which postulates matter to be infinitely divisible and its physical laws to be

deterministic. Test-design language must be silent about such claims, and

must be given the status that Heisenberg called “everyday” language, which

is silent, i.e., vague, about these Newtonian claims. Furthermore the

statements of the quantum theory proposed for testing are too hypothetical to

function as definitions except for the developer and other advocates of the

theory, who may believe in the theory as strongly as they believe in the truth

of the test-design statements.

But for all the critical researchers for whom the test is contingent and

functions as a decision procedure, the semantical consequence of the logical

independence and greater hypothetical status of a theory proposed for testing

relative to the universal statements of test design, is that each of the terms

common to both the test-design statements and theory statements have their

semantics defined only in relation to the meanings of the other terms in the

test-design statements, such that they characterize the subject matter of the

experiment, but do not have their semantics defined in relation to the

meanings of the terms in the theory proposed for testing. In other words by

strategic decision for testing, the theory statements are not included in the

same semantical description list as the test-design statements, even though

both sets of statements are mutually consistent and contain the same common

subject terms. The meaning of each term common to the test-design and

theory statements is therefore vague with respect to the meanings of the other

terms of the theory.

And on the artifactual thesis of the semantics of language the

observation language in turn is merely the test-design statements with their

logical quantification changed from universal to particular, to enable their

application to describe the particular ongoing or historical experiment

performance. The test-design statements similarly supply the vocabulary that

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describes the observed test outcome, especially if the outcome contradicts

and thus falsifies the claims of the tested theory.

Test Language After Test Execution

Consider next the language of the empirical test after the test is

executed and its outcome is known. When the test is executed, a falsifying

test outcome produces no semantical change except for the developer and

advocates of the tested theory, who had been convinced of the theory’s truth,

and who decide to reconsider their belief in the theory due to the test

outcome. The latter’s belief revision causes a semantical change. But a

nonfalsifying outcome produces a semantical change, especially for the critics

of the theory for whom the test is a decision procedure. After the test the

theory no longer has the greater hypothetical status that it formerly had

merely as a proposal, but assumes the status of a law that may operate in an

explanation, which is neither more nor less contingent than other accepted

universal empirical statements including the test-design statements. The

semantical outcome is that both the test-design statements and the theory

statements (now elevated to the status of a law) are semantical rules

exhibiting the composition of the meanings of the univocal terms common to

both sets of statements. Those component parts contributed by the test-

design statements remain included. But the semantical descriptions for these

terms now include not only the test-design statements but also the statements

constituting the tested and nonfalsified former theory. These former theory

statements are additional information learned from the successful test

outcome that resolves some of the vagueness in the vocabulary terms

common to both the theory and the test-design statements.

In summary: the descriptive terms common to both test-design and

theory statements have part of their semantics defined by the test-design

statements throughout the test, both before, during, and after the test is

executed. And these common terms have their semantics augmented and thus

defined by the statements of the tested and nonfalsified former theory added

after the test, such that the test-design concepts have their vagueness resolved

by the tested and nonfalsified former theory.

Semantics and Quantum Theory Tests

In Heisenberg’s doctrine of closed-off theories the naturalistic

philosophy of language requires retention of the Newtonian concepts for

observation in any quantum-theory experiments. But the resulting

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equivocation is unnecessary. Newtonian concepts are never involved, since

the Newtonian theory is a falsified microphysical theory or at least an

alternative to the quantum theory. Before the test outcome is known it is

sufficient to use a vaguer or less precise vocabulary that Heisenberg calls

“everyday” words used by physicists, in order to describe the

experimental set up, which is a macrophysical phenomenon. The

meanings of these “everyday” concepts are vague, because they do not

describe the fundamental constitution of matter. After the test outcome is

known, the tested and nonfalsified quantum theory is recognized as

empirically adequate, and the vagueness in these everyday concepts is

resolved by the equations constituting the quantum theory. The quantum

mechanics is the tested and nonfalsified former theory, which after the test as

a law became a semantical rule contributing meaning parts to the complex

meanings of the univocal terms used to describe the experimental set up such

as the Stern-Gerlach or two-slit apparatuses. This effectively makes the

meanings quantum concepts, whether or not quantum effects are empirically

detectable or operative in the description of the macroscopic features of the

experimental set up.

Even if some Newtonian laws are employable for their now known

lesser truth, in order for this resolution of vagueness to occur in the terms

used for description of the macroscopic features of the experimental set up, it

is not necessary for the Newtonian macrophysical laws to be made logical

extensions of quantum mechanics by logical reduction procedures, because

the Newtonian theory is falsified as a microphysical theory. Nor is it

necessary for the Newtonian macrophysical laws to be replaced by

macrophysical laws that are an extension of the quantum laws. The univocal

quantum semantics neither implies nor requires any logical reductionist or

extensional development of macrophysical quantum mechanics, i.e., a

macrophysical theory that is deductively or reductively a logical extension of

the microphysical quantum mechanics. It is sufficient merely that the

scientist realize that the nonfalsifying test outcome has made quantum

mechanics and not classical mechanics an empirically warranted

microphysical theory.

Heisenberg’s doctrine of closed-off theories is incorrect, and Einstein’s

semantical thesis expressed in his aphorism to Heisenberg is correct, because

the vocabulary used for macroscopic observation after quantum mechanics’

acceptance is a univocal vocabulary with meaning parts contributed by

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quantum mechanics. The descriptive terms in the equations of the quantum

mechanics contribute to, and thereby resolve some of the vagueness in the

meaning complex associated with the descriptive terms used for observation.

Thus as Heisenberg maintained, quantum mechanics decides what the

scientist observes in the Wilson cloud chamber. The macrophysical

description is not antilogous to the microphysical quantum mechanics

including the indeterminacy relations. In summary the quantum semantic

values are included in the univocal meaning complexes associated with

the observation description, and the Newtonian concepts were never

included, because the macrophysical description never affirmed a

Newtonian microphysical theory.

Heisenberg’s Last Statements on Semantics

In his “Remarks on the Origin of the Relations of Uncertainty” in a

memorial volume dedicated to him titled The Uncertainty Principle and

Foundations of Quantum Mechanics (1977), which was in press at the time

of his death in 1976, Heisenberg says in this brief four-page article that there

have been attempts to replace the traditional language with its classical

concepts by a new language which would be better adapted to the

mathematical formalism of quantum theory. But he adds that during the

preceding fifty years, physicists have preferred to use the traditional language

in describing their experiments with the precaution that the limitations given

by the indeterminacy relations should “always be kept in mind”. He

concludes that a “more precise” language has not been developed and in fact

it is not needed, since there seems to be general agreement about the

conclusions and predictions drawn from any given experiment in the field.

In other words the semantics of terms like “momentum” and “position”,

“wave” and “particle” have evolved much like the semantics of the term

“atom” has evolved in the history of physics, even as the vocabulary has been

retained.

Regrettably Heisenberg never repudiated his doctrine of closed-off

theories. But contrary to his doctrine of closed-off theories, Heisenberg’s

statement that the contemporary physicist must keep quantum effects “in

mind” when the physicist is describing macrophysical objects, even while not

explicitly accounting for quantum effects that are experimentally undetectable

in the circumstances, is ipso facto a semantical change in the univocal

vocabulary used to describe experiments due to the development of quantum

mechanics. In other words a language in which the limitations given by the

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indeterminacy relations are “always be kept in mind”, means that a “more

precise” language with a less vague semantics has in fact been evolved. This

semantical evolution consists in the fact that the concepts employed for

observational description contain component parts, i.e., semantic values,

contributed from quantum mechanics. That is how the limitations of the

indeterminacy relations are “always kept in mind”: they have become built

into the semantics of those terms, even when those terms are used to

describe macrophysical observations including but not limited to cloud

chamber tracks.

Double-Think Rejected

Heisenberg’s semantical theory of equivocation in his and Bohr’s

philosophy of observation language is the result of the acceptance of the

naturalistic philosophy of the semantics together with the assumption that

meanings are simple, indivisible wholes. However, all such views are

untenable, because they imply what can only be called “double think”. The

equivocation thesis demands that the modern physicist indulge in a contrived

cognitive duplicity with himself, a pretense at simultaneously both knowing

and not knowing the modern quantum theory. But concepts are not known

like physical objects to which one may simply close one’s eyes; they are

knowledge. Scientists never did in practice carry on the kind of cognitive

duplicity that the equivocation semantical theses require, and since the

ascendancy of the contemporary pragmatism, philosophers no longer expect

that they should.

Heisenberg might have obtained greater utility from his insightful idea

of “everyday” concepts, had he rejected Bohr’s philosophy of observation

language, and realized that neither these “everyday” concepts nor the

Newtonian concepts nor any other concepts are inherently observational.

Heisenberg’s term “everyday” is admittedly awkward, because the everyday

man in the street does not perform quantum experiments. But in the

pragmatist perspective Heisenberg’s “everyday” concepts are distinctive only

because they are vague in a very strategic fashion: they are the concepts used

in test-design statements, and are vague relative to the concepts in the

theories proposed for testing prior to execution of the test and prior to the

production of a nonfalsifying test outcome. More specifically, in the case

of the quantum-mechanics experiments, everyday test-design concepts are

vague because they are not defined by either the Newtonian or the quantum

theories or of any other proposed microphysical theory prior to the execution

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of the tests. After execution of the test and after production of a

nonfalsifying test outcome, the vagueness of the “everyday” concepts is

resolved with respect to microphysical phenomena and become quantum

concepts, such as Heisenberg used for observing the electron tracks in the

cloud chamber.

In “On the Methods of Theoretical Physics” in Ideas and Opinions

(1933) Einstein said that if you want to find out anything from the theoretical

physicists about the methods they use, stick closely to one principle: don’t

listen to their words, but rather fix your attention on their deeds. This is good

advice for anyone attempting to understand Heisenberg’s writings in

philosophy of science. The philosophy of language that was instrumental to

Heisenberg’s “deeds”, i.e., his development of his indeterminacy relations as

a result of Einstein’s influence and that is chronicled in his autobiographical

works, is historically more important and more revealing than the “words” he

expounded as a result of Bohr’s influence and set forth as his doctrine of

closed-off theories, because pragmatism is the philosophy of language that

Heisenberg practiced.

Quantum physicists are like the Biblical characters who had been

driven out of the Garden of Eden. They have eaten from the forbidden fruit

of the tree of quantum knowledge, the fruit forbidden by Newtonian

physics. They have consumed such findings as uncertainty, duality, and

nonlocality, so that today they simply know too much to return to the their

former state of blissful nineteenth-century innocence, in which Newtonian

concepts had been definitive of the semantics for observational reporting.

Now the semantics they must use in their conceptualization of the sense

stimuli that produce their observational reporting language, is penetrated,

permeated and suffused with semantic values from quantum theory.

A New Reductionist Language Developed

Roland Omnès is presently Professor Emeritus of Theoretical Physics

in the Faculté des sciences at Orsay at the Université Paris. In his

Understanding Quantum Mechanics (1999) Omnès writes that since the

1980’s there has been a renewal in both experiments and theory due to a

transition from a period when Bell’s ideas and the hidden variables issues

were dominant, to the current period when the interpretation of Copenhagen

quantum mechanics has become the dominant interest.

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Omnès says that the renewal involves three theoretical ideas: the

decoherence effect, the emergence of classical physics from quantum theory,

and the constitution of a universal language of “interpretation” by means of

consistent histories. The decoherence effect, which was recently observed in

recent experiments by Jean-Michael and Serge Haroche, explains the absence

of macrophysical environmental interference and solves the Schrödinger’s cat

problem. The emergence of classical physics from quantum theory using the

Hilbertian framework explains the relation between quantum and classical

physics, and reconciles determinism with probabilism. The constitution of a

universal language of “interpretation” by the method of consistent histories

provides a logical structure for quantum and classical physics, and it supplies

the universal language of “interpretation” initially sought by the members of

Bohr’s Copenhagen Institute for Physics, but which Bohr’s complementarity

cannot supply. Omnès has been instrumental in developing the consistent

histories and quantum decoherence approaches. He writes that when these

three ideas are combined, they provide a genuine theory of interpretation, in

which everything is derived directly from basic principles using the Hilbert-

space framework to deduce theorems including the rules of measurement

theory, and he sets forth a set of axioms.

It may be said that Omnès’ deductive system not only resolves the

relatively vague semantics of Heisenberg’s “everyday” language, but because

it is deductive, it further resolves the vagueness in the semantics of the

vocabulary in both macrophysics and microphysics. Omnès’ logical

integration of physical theory may satisfy long-standing psychological

yearnings for intellectual coherence expressed by both physicists and

philosophers. Yale University’s Norwood Russell Hanson would likely have

dismissed Omnès and his ilk as mere “axiomitizers”.

Heisenberg’s Practice of Ontological Relativity

Unlike Bohr, Heisenberg effectively practiced what Quine called

“ontological relativity”, when he reported that he interpreted the quantum

mechanics equations realistically by replicating Einstein’s realist

interpretation for special relativity. Heisenberg said the “decisive step” in the

development of special relativity was Einstein’s rejecting the distinction

between apparent time and actual time in the interpretation of the Lorentz

transformation equation, taking Lorentz’s apparent time to be physically real

time, and rejecting the Newtonian absolute time as real time. Heisenberg said

he took the same kind of decisive step, when he inverted the question of how

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to pass from an experimentally given situation to its mathematical represen-

tation by affirming that only those states represented as vectors in Hilbert

space can occur in nature and be realized experimentally. Heisenberg’s

indeterminacy principle says that no quantum-mechanical state can be

dispersion free for every variable. He thus believed that his decisive step

affirms that microphysical reality is nondeterministic. He likewise maintains

that Young’s two-slit experiment affirms the duality thesis of quantum

mechanics, and that wave and particle are manifestations of the same entity

that is indeterminate until subject to a measurement action.

Hanson and Heisenberg

In his Patterns of Discovery (1958) Norwood Russell Hanson (1924-

1967) dismissed what he called Bohr’s “naïve epistemology”, and like

Einstein he believed that observation is what Hanson called “theory laden”.

It may be said that Hanson’s philosophy of quantum theory is what

Heisenberg could have formulated, had Heisenberg rejected Bohr’s

naturalistic semantics, which Heisenberg used for his doctrine of closed-off

theories, and instead followed through on Einstein’s aphorism that theory

decides what the physicist can observe.

Hanson defended the Copenhagen duality thesis by reference to the

mathematical transformation theory developed in 1928 by Paul A. Dirac

(1902-1984), who was a theoretical physicist at Cambridge University, and

who shared the Nobel Memorial Prize for physics in 1933 with Schrödinger.

Hanson had interviewed Dirac at Cambridge for writing his Concept of the

Positron (1963). Dirac’s transformation theory enables physicists to exhibit

the wave-particle duality by mathematically transforming the wave

description into the quantum description and vice versa. Hanson thus says

that in the formalisms for modern quantum physics there is a logicolinguistic

obstacle to any attempt to describe with precision the total state of an

elementary particle, such that quantum mechanics makes the dualistic

ontology the only conceivable one. This thesis of Hanson echoes

Heisenberg’s thesis of false questions set forth in his paper “Questions of

Principle” (1935), in which he says that the system of mathematical axioms of

quantum mechanics entitles the physicist to regard the question the

simultaneous determination of position and impulse values as a false problem,

just as Einstein’s relativity theory makes the question of absolute time a false

question in the sense that they are devoid of meaning.

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Hanson’s philosophy is discussed in BOOK VII below.

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